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Search: id:A096163
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| A096163 |
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Primes p of the form qrs + 1 where q, r and s are distinct primes. |
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+0
1
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| 31, 43, 67, 71, 79, 103, 131, 139, 191, 223, 239, 283, 311, 367, 419, 431, 439, 443, 499, 599, 607, 619, 643, 647, 659, 683, 743, 787, 823, 827, 907, 947, 971, 1031, 1039, 1087, 1091, 1103, 1163, 1223, 1259, 1399, 1427, 1447, 1499, 1511, 1543, 1559, 1571, 1579
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Each composite number qrs = a(n)-1 is a squarefree 3-almost prime. This sequence is a subsequence of A078330 which, besides having 3 as its first term, first differs by including 2311 = 2*3*5*7*11 + 1 (a squarefree 5-almost prime plus 1).
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PROGRAM
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(PARI) /* Here are five equivalent PARI programs */ forprime(p=2, 2400, if(moebius(p-1)==-1 && omega(p-1)==3, print1(p, ", "))) forprime(p=2, 2400, if(moebius(p-1)==-1 && bigomega(p-1)==3, print1(p, ", "))) forprime(p=2, 2400, if(bigomega(p-1)==3 && omega(p-1)==3, print1(p, ", "))) forprime(p=2, 2400, if(omega(p-1)==3 && issquarefree(p-1), print1(p, ", "))) forprime(p=2, 2400, if(bigomega(p-1)==3 && issquarefree(p-1), print1(p, ", ")))
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CROSSREFS
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Cf. A078330 (primes p with mu(p-1) = -1).
Sequence in context: A067467 A069455 A118637 this_sequence A139883 A060834 A060844
Adjacent sequences: A096160 A096161 A096162 this_sequence A096164 A096165 A096166
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 18 2004
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